.. range operator
>< Cartesian product
?, Man search online help system
Abs absolute value of a number
Adjoint adjoint matrix
Alias define aliases for package names
Alias In temporarily override global aliases
Aliases list of global aliases
Append append an object to an existing list
Ascii convert between characters and ascii code
Bin binomial coefficient
BinExp, EvalBinExp binomial expansion
Block group several commands into a single command
BlockMatrix create a block matrix
Break break out of a loop
BringIn bring in objects from another ring
Call apply a function to given arguments
Cast type conversion
Catch catch an error
CFApprox, CFApproximants, ContFrac continued fractions
Characteristic the characteristic of a ring
Ciao quit CoCoA
Clear clear the working memory or a ring-bound memory
Close close a device
CocoaLimits limits on exponents and ring characteristics
CocoaPackagePath returns the path to the CoCoA packages
Coefficients list of coefficients of a polynomial or vector
CoeffOfTerm coefficient of a term of a polynomial or vector
Colon, :, HColon ideal or module quotient
ColumnVectors the list of column vectors of a matrix
Comp the N-th component of a list
Comps list of components of a vector
Concat, ConcatLists concatenate lists or lists of lists, respectively
Cond conditional expression
Contrib list of contributors to CoCoA
Count count the objects in a list
CurrentRing the current ring
Dashes returns string of dashes
Date the date
DecimalStr convert rational number to decimal string
Define define a function
Defined check if an expression has been defined
Deg the degree of a polynomial or vector
DegLexMat, DegRevLexMat, LexMat, XelMat matrices for std. term-orderings
Delete delete variables from the working memory
DensePoly the sum of all power-products of a given degree
Der the derivative of a rational function
Describe information about an expression
Destroy delete rings
Det the determinant of a matrix
Diff returns the difference between two lists
Dim the dimension of a ring or quotient object
Discriminant the discriminant of a polynomial
Distrib the distribution of objects in a list
Div, Mod quotient and remainder for integers
DivAlg division algorithm
E_ canonical vector
Elim eliminate variables
EqSet checks if the set of elements in two lists are equal
Equals returns a string of equal signs
EquiIsoDec equidimensional isoradical decomposition
Error return an error message
Eval substitute numbers or polynomials for indeterminates
EvalHilbertFn evaluate the Hilbert function
Fact factorial function
Factor factor a polynomial
Fields list the fields of a record
First the first N elements of a list
FirstNonZero, FirstNonZeroPos the first non-zero entry in a vector
Flatten flatten a list
FloatApprox approx. of rational number of the form M*10^E
FloatStr, MantissaAndExponent convert rational number to a float string
For loop command
Foreach loop command
Format convert object to formatted string
Fraction returns the quotient of its arguments
Function return a function
Functions list the functions of a package
GB.Complete Complete an interactive Groebner-type calculation
GB.GetBettiMatrix returns the Betti matrix computed so far
GB.GetNthSyz returns the part of the Nth syzygy module computed so far
GB.GetNthSyzShifts shifts of the Nth syzygy module computed so far
GB.GetRes returns the resolution computed so far
GB.GetResLen returns the length of the resolution computed so far
GB.ResReport status of an interactive resolution calculation
GB.Start_GBasis start interactive Groebner basis computation
GB.Start_MinGens start interactive minimal generator calculation
GB.Start_MinSyzMinGens start interactive calc., min. syzs. of min. gens.
GB.Start_Res start interactive resolution computation
GB.start_Syz start interactive syzygy computation
GB.start_SyzMinGens start interactive calc. of syzygies of min. gens.
GB.Stats status of an interactive Groebner-type calculation
GB.Step, GB.Steps take steps in an interactive Groebner-type calculation
GBasis calculate a Groebner basis
GBM, HGBM intersection of ideals for zero-dimensional schemes
GCD, LCM greatest common divisor, least common multiple
GenericPoints random projective points
GenRepr representation in terms of generators
Gens list of generators of an ideal
Get read characters from a device
GetErrMesg returns the message associated with an error
Gin generic initial ideal
GlobalMemory contents of global memory
H.Browse browse the online help system
H.Commands list commands according to type
H.Man search online help system (see "?, Man")
H.OutCommands print command descriptions to a file
H.OutManual print the online manual to a file
H.SetMore, H.UnSetMore more-device for online help
H.Syntax display the syntax of a command
H.Tips quick tips for using online help
H.Toc display the Table Of Contents of the online manual
H.Tutorial run the CoCoA tutorial
Head the first element of a list
Help extend online help for user-defined functions
Hilbert the Hilbert function
HilbertBasis Hilbert basis for a monoid
HilbertPoly the Hilbert polynomial
HIntersection, HIntersectionList intersection of ideals
Homogenized homogenize with respect to an indeterminate
HVector the h-vector of a ring or quotient object
Ideal convert an expression into an ideal
IdealAndSeparatorsOfPoints ideal and separators for affine points
IdealAndSeparatorsOfProjectivePoints ideal and separators for points
IdealOfPoints ideal of a set of affine points
IdealOfProjectivePoints ideal of a set of projective points
Identity the identity matrix
If conditional statement
ILogBase integer part of the logarithm
Image ring homomorphism
In create a list satisfying given conditions
Indet individual indeterminates
IndetInd the index of an indeterminate
IndetIndex index of an indeterminate
IndetName the name of an indeterminate
Indets list of current indeterminates
Insert, Remove insert or remove an object in a list
Interpolate interpolating polynomial
Interreduce, Interreduced interreduce a list of polynomials or vectors
Intersection, IntersectionList intersect lists, ideals, or modules
Inverse multiplicative inverse
IO.SprintTrunc convert to a string and truncate
Iroot integer part of r-th root of an integer
IsEven, IsOdd test whether an integer is even or odd
IsHomog test whether given polynomials are homogeneous
IsIn check if one object is contained in another
IsNumber checks if the argument is a number
IsPosTo, IsToPos checks the module term-ordering of a ring
IsPrime prime integer test
Isqrt computes the (truncated) square root of an integer
IsStable, IsStronglyStable, IsLexSegment checks if an ideal is stable (resp. strongly stable or a lex-segment)
IsSubset checks if the elements of one list are a subset of another
IsTerm checks if the argument is a term
IsZero test whether an object is zero
Jacobian the Jacobian of a list of polynomials
Last the last N elements of a list
Latex LaTeX formatting
LC the leading coefficient of a polynomial or vector
Len the length of an object
LinKer find the kernel of a matrix
LinSol find a solution to a linear system
List convert an expression into a list
LM the leading monomial of a polynomial or vector
Log the list of exponents of the leading term of a polynomial
LogToTerm returns a monomial (power-product) with given exponents
LPos the position of the leading power-product in a vector
LPP the leading power-product of a polynomial or vector
LT the leading term of an object
MapDown convert a constant polynomial to a number
Mat convert an expression into a matrix
Max, Min a maximum or minimum element of a sequence or list
MDeg multi-degree of an polynomial
Memory contents of local memory or ring-bound memory
MinGens list minimal generators
Minimalize, Minimalized remove redundant generators
Minors list of minor determinants of a matrix
MinSyzMinGens minimal generators of syzygies of minimal generators
Mod2Rat reconstructing rationals from modular integers
Module convert an expression into a module
Monic divide polynomials by their leading coefficients
Monomials the list of monomials of a polynomial or vector
MonsInIdeal ideal generated by the monomials in an ideal
More print a string, N lines at a time
Multiplicity the multiplicity (degree) of a ring or quotient object
NewId create a new identifier
NewList create a new list
NewMat create a new matrix
NewVector create a new vector
NextPrime find the next largest prime number
NF normal form
NFsAreZero test if normal forms are zero
NonZero remove zeroes from a list
Not, And, Or boolean operators
NR normal reduction
Num, Den numerator, denominator
NumComps the number of components of a vector
NumIndets number of indeterminates
OpenIFile, OpenOFile open input or output file
OpenIString, OpenOString open input or output string
OpenLog, CloseLog open or close a log of a CoCoA session
Option status of a panel option
Ord matrix defining a term-ordering
Packages list of loaded packages
Panel print status of a panel's options
Panels list of CoCoA panels
Partitions partitions of an integer
Pfaffian the Pfaffian of a skew-symmetric matrix
PkgName returns the name of a package
Poincare, HilbertSeries the Poincare series
Poly convert an expression into a polynomial
PrimaryDecomposition primary decomposition of an ideal
Print On print to an output device
Print, PrintLn print the value of an expression
Product, Sum the product or sum of the elements of a list
Quit quit CoCoA
QuotientBasis vector space basis for zero-dimensional quotient rings
QZP, ZPQ change field for polynomials and ideals
Radical radical of an ideal
RadicalOfUnmixed radical of an unmixed ideal
Rand random integer
Randomize, Randomized randomize the coefficients of a given polynomial
Rank rank of a module
RealRootRefine refine a root of a univariate polynomial over Q
RealRoots computes a root of a univariate polynomial over Q
Record create a record
ReducedGBasis compute a reduced Groebner basis
Repeat loop command
Res free resolution
Reset reset panels and random number seed to defaults
ResetPanels reset panels to their default values
Resultant the resultant of two polynomials
Return exit from a structured command
Reverse, Reversed reverse a list
Ring returns the ring with a given name
RingEnv name of the current ring
RingEnvs names of all defined rings
RootBound bound on roots of a polynomial over Q
Saturation, HSaturation saturation of ideals
ScalarProduct scalar product
Seed seed for Rand
SeparatorsOfPoints separators for affine points
SeparatorsOfProjectivePoints separators for projective points
Set remove duplicates from a list
Set, Unset set and unset panel options
Shape extended list of types involved in an expression
Size the amount of memory used by an object
Skip does nothing
Sort, Sorted sort a list
SortBy, SortedBy sort a list
Source, << read commands from a file or device
Spaces return a string of spaces
Sprint convert to a string
StarPrint print polynomial with *'s for multiplications
Starting list functions starting with a given string
Submat submatrix
Subsets returns all sublists of a list
Subst substitute values for indeterminates
Support the list of terms of a polynomial or vector
Sylvester the Sylvester matrix of two polynomials
Syz syzygy modules
SyzMinGens syzygy module for a set of minimal generators
SyzOfGens syzygy module for a given set of generators
Tag returns the tag string of an object
Tagged, Untagged, @ tag or untag an object for pretty printing
Tail remove the first element of a list
TensorMat returns the tensor product of two matrices
Toric saturate toric ideals
Toric.CheckInput check input to Toric
Transposed the transposition of a matrix
Tuples N-tuples
Type the data type of an expression
TypeOfCoeffs type of the coefficients of the current ring
Types lists all data types
Use command for making a ring active
Using perform commands in non-active ring
Var function calls by reference, other complex referencing
Vector create a vector
WeightsList first row of the weights matrix
WeightsMatrix matrix of generalized weights for indeterminates
While loop command
WithoutNth removes the N-th component from a list
WLog weighted list of exponents